The Structure of Weighting Coefficient Matrices of Harmonic Differential Quadrature and Its Applications

TL;DR

This paper investigates the structure of weighting coefficient matrices in Harmonic Differential Quadrature, revealing their centrosymmetric or skew centrosymmetric nature, which can significantly reduce computational effort in applications.

Contribution

It identifies the matrix structures in HDQ and demonstrates how leveraging these properties can cut computational costs by up to 75%.

Findings

Matrices are either centrosymmetric or skew centrosymmetric.

Properties of these matrices are briefly discussed.

Computational effort can be reduced by up to 75%.

Abstract

The structure of weighting coefficient matrices of Harmonic Differential Quadrature (HDQ) is found to be either centrosymmetric or skew centrosymmetric depending on the order of the corresponding derivatives. The properties of both matrices are briefly discussed in this paper. It is noted that the computational effort of the harmonic quadrature for some problems can be further reduced up to 75 per cent by using the properties of the above-mentioned matrices.